Question

ХЕЛП!!! Реши задачу, выделяя три этапа математического моделирования: «Производительность труда мастера на 12 деталей в час больше, чем производительность труда ученика. Мастер работал 3 ч., а ученик — 6 ч. Определи количество деталей в час, изготавливаемых мастером, если он изготовил деталей в 2 раза больше, чем ученик». Ответ: количество деталей в час, изготавливаемых мастером

Answer 1

Mathematical Modeling of Labor Productivity

To solve the given problem, we need to determine the number of parts produced per hour by the master. Let's break down the problem into three stages of mathematical modeling:

Stage 1: Defining Variables - Let's assume the productivity of the master is represented by the variable M (in parts per hour). - Similarly, the productivity of the apprentice is represented by the variable A (in parts per hour).

Stage 2: Formulating Equations - According to the problem statement, the productivity of the master is 12 parts per hour more than the productivity of the apprentice. Therefore, we can write the equation as: - M = A + 12 Stage 3: Solving the Equations - The master worked for 3 hours, so the total number of parts produced by the master is 3M. - The apprentice worked for 6 hours, so the total number of parts produced by the apprentice is 6A. - According to the problem statement, the master produced twice as many parts as the apprentice. Therefore, we can write the equation as: - 3M = 2(6A)

Now, let's solve the equations to find the value of M, which represents the number of parts produced per hour by the master.

Substituting the value of M from equation (1) into equation (2), we get: - 3(A + 12) = 2(6A) - 3A + 36 = 12A - 36 = 9A - A = 4

Substituting the value of A back into equation (1), we can find the value of M: - M = A + 12 - M = 4 + 12 - M = 16

Therefore, the master produces 16 parts per hour.

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